Sampling Quantum Nonlocal Correlations with High Probability

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of (Formula presented.), where the previous vectors are sampled according to the Haar measure in the unit sphere of (Formula presented.). In particular, we prove the existence of an (Formula presented.) such that if (Formula presented.), (Formula presented.) is nonlocal with probability tending to 1 as (Formula presented.), while for (Formula presented.), (Formula presented.) is local with probability tending to 1 as (Formula presented.).

Three-dimensional inverse modelling of magnetic anomaly sources based on a genetic algorithm.

We present a modelling method to estimate the 3-D geometry and location of homogeneously magnetized sources from magnetic anomaly data. As input information, the procedure needs the parameters defining the magnetization vector (intensity, inclination and declination) and the Earth's magnetic field direction. When these two vectors are expected to be different in direction, we propose to estimate the magnetization direction from the magnetic map. Then, using this information, we apply an inversion approach based on a genetic algorithm which finds the geometry of the sources by seeking the optimum solution from an initial population of models in successive iterations through an evolutionary process. The evolution consists of three genetic operators (selection, crossover and mutation), which act on each generation, and a smoothing operator, which looks for the best fit to the observed data and a solution consisting of plausible compact sources. The method allows the use of non-gridded, non-planar and inaccurate anomaly data and non-regular subsurface partitions. In addition, neither constraints for the depth to the top of the sources nor an initial model are necessary, although previous models can be incorporated into the process. We show the results of a test using two complex synthetic anomalies to demonstrate the efficiency of our inversion method. The application to real data is illustrated with aeromagnetic data of the volcanic island of Gran Canaria (Canary Islands).

Search for signatures of magnetically-induced alignment in the arrival directions measured by the Pierre Auger Observatory

We present the results of an analysis of data recorded at the Pierre Auger Observatory in which we search for groups of directionally-aligned events (or 'multiplets') which exhibit a correlation between arrival direction and the inverse of the energy. These signatures are expected from sets of events coming from the same source after having been deflected by intervening coherent magnetic fields. The observation of several events from the same source would open the possibility to accurately reconstruct the position of the source and also measure the integral of the component of the magnetic field orthogonal to the trajectory of the cosmic rays. We describe the largest multiplets found and compute the probability that they appeared by chance from an isotropic distribution. We find no statistically significant evidence for the presence of multiplets arising from magnetic deflections in the present data. (C) 2011 Elsevier B.V. All rights reserved.

The Lateral Trigger Probability function for the Ultra-High Energy Cosmic Ray showers detected by the Pierre Auger Observatory

In this paper we introduce the concept of Lateral Trigger Probability (LTP) function, i.e., the probability for an Extensive Air Shower (EAS) to trigger an individual detector of a ground based array as a function of distance to the shower axis, taking into account energy, mass and direction of the primary cosmic ray. We apply this concept to the surface array of the Pierre Auger Observatory consisting of a 1.5 km spaced grid of about 1600 water Cherenkov stations. Using Monte Carlo simulations of ultra-high energy showers the LTP functions are derived for energies in the range between 10(17) and 10(19) eV and zenith angles up to 65 degrees. A parametrization combining a step function with an exponential is found to reproduce them very well in the considered range of energies and zenith angles. The LTP functions can also be obtained from data using events simultaneously observed by the fluorescence and the surface detector of the Pierre Auger Observatory (hybrid events). We validate the Monte Carlo results showing how LTP functions from data are in good agreement with simulations.